Basic Math Examples

$- 3 \sqrt[4]{243} + \sqrt{48} - \sqrt{108} + \sqrt{54}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $243$ as $3^{4} \cdot 3$ .

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Step 1.1.1

Factor $81$ out of $243$ .

$- 3 \sqrt[4]{81 (3)} + \sqrt{48} - \sqrt{108} + \sqrt{54}$

Step 1.1.2

Rewrite $81$ as $3^{4}$ .

$- 3 \sqrt[4]{3^{4} \cdot 3} + \sqrt{48} - \sqrt{108} + \sqrt{54}$

Step 1.2

Pull terms out from under the radical.

$- 3 (3 \sqrt[4]{3}) + \sqrt{48} - \sqrt{108} + \sqrt{54}$

Step 1.3

Multiply $3$ by $- 3$ .

$- 9 \sqrt[4]{3} + \sqrt{48} - \sqrt{108} + \sqrt{54}$

Step 1.4

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 1.4.1

Factor $16$ out of $48$ .

$- 9 \sqrt[4]{3} + \sqrt{16 (3)} - \sqrt{108} + \sqrt{54}$

Step 1.4.2

Rewrite $16$ as $4^{2}$ .

$- 9 \sqrt[4]{3} + \sqrt{4^{2} \cdot 3} - \sqrt{108} + \sqrt{54}$

Step 1.5

Pull terms out from under the radical.

$- 9 \sqrt[4]{3} + 4 \sqrt{3} - \sqrt{108} + \sqrt{54}$

Step 1.6

Rewrite $108$ as $6^{2} \cdot 3$ .

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Step 1.6.1

Factor $36$ out of $108$ .

$- 9 \sqrt[4]{3} + 4 \sqrt{3} - \sqrt{36 (3)} + \sqrt{54}$

Step 1.6.2

Rewrite $36$ as $6^{2}$ .

$- 9 \sqrt[4]{3} + 4 \sqrt{3} - \sqrt{6^{2} \cdot 3} + \sqrt{54}$

Step 1.7

Pull terms out from under the radical.

$- 9 \sqrt[4]{3} + 4 \sqrt{3} - (6 \sqrt{3}) + \sqrt{54}$

Step 1.8

Multiply $6$ by $- 1$ .

$- 9 \sqrt[4]{3} + 4 \sqrt{3} - 6 \sqrt{3} + \sqrt{54}$

Step 1.9

Rewrite $54$ as $3^{2} \cdot 6$ .

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Step 1.9.1

Factor $9$ out of $54$ .

$- 9 \sqrt[4]{3} + 4 \sqrt{3} - 6 \sqrt{3} + \sqrt{9 (6)}$

Step 1.9.2

Rewrite $9$ as $3^{2}$ .

$- 9 \sqrt[4]{3} + 4 \sqrt{3} - 6 \sqrt{3} + \sqrt{3^{2} \cdot 6}$

Step 1.10

Pull terms out from under the radical.

$- 9 \sqrt[4]{3} + 4 \sqrt{3} - 6 \sqrt{3} + 3 \sqrt{6}$

Step 2

Subtract $6 \sqrt{3}$ from $4 \sqrt{3}$ .

$- 9 \sqrt[4]{3} - 2 \sqrt{3} + 3 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 9 \sqrt[4]{3} - 2 \sqrt{3} + 3 \sqrt{6}$

Decimal Form:

$- 7.96029850 \dots$